Question

For a reaction $A \rightarrow 2 B + C$ the half lives are $100 \,s$ and $50 \,s$ when the concentration of reactant $A$ is $0.5$ and $1.0 \,mol \,L ^{-1}$ respectively. The order of the reaction is _______ (Nearest Integer)

Answer 1

$ t _{\frac{1}{2}} \propto \frac{1}{\left[ A _0\right]^{ n -1}} $
$ {[100] \propto \frac{1}{(0.5)^{ n -1}}}$
$ (50) \propto \frac{1}{(1)^{n-1}} $
${[2]^1=\left[\frac{1}{0.5}\right]^{n-1}}$
$ {[2]^1=[2]^{n-1}} $
$ n-1=1 $
$ n=2$ order $=2$